The scientific method is a generalized approach that many people believe describes how scientists investigate the world and produce knowledge about it. As it is most often described, the method is distinguished by its use of controlled experiments and the requirement that results be reproducible. Because many people see mathematicians as working scientifically, however, some regard physical experiments as inessential and argue that proofs figure equivalently in mathematics.

Scientists and other scholars disagree about whether any single method, no matter how abstractly it might be expressed, can describe how all scientific knowledge is produced. They also disagree about the extent to which certain popular notions of the scientific method apply to any of the knowledge that scientists have produced.

In the judicial system and in debates of government policy, the results of research often are evaluated in terms of whether the researchers arrived at them by "the scientific method." In such contexts, it is said that results arrived at by other means should be rejected as products of "junk science" or "pseudoscience."

The goals of distinguishing good science from bad and of identifying a recipe for progress offer justification enough for many to pursue the question of method. For other thinkers and observers, which include philosophers, historians, sociologists and anthropologists, the motivation is a more basic curiosity about how science works.

No scientist claims that there is a single algorithm-like procedure with which they approach every scientific problem. Some would say that there is a general prescription that describes how science operates most of the time, however. It entails these actions:

Observe: Collect evidence and make measurements relating to the phenomenon you intend to study.

Hypothesize: Invent a hypothesis explaining the phenomenon that you have observed.

Predict: Use the hypothesis to predict the results of new observations or measurements. Often, advanced mathematical and statistical hypothesis testing techniques are used to design experiments that attempt to effectively test the plausibility of hypotheses.

Verify: Perform experiments to test those predictions. Attempting to experimentally falsify hypotheses is thought by many to be a better choice of term here.

Evaluate: If the experiments contradict your hypothesis, reject it and form another. If the results are compatible with predictions, make more predictions and test it further.

Publish: Tell other people of your ideas and results, and encourage them to verify the claims themselves, in particular by inviting them to challenge your reasoning and check that your experimental results can be repeated. This process is known as peer review.

These steps are repeated continually, building a larger and larger set of well-tested hypotheses to explain more and more phenomena. These steps are not necessarily always followed in the pattern shown above. For example, theoretical physicists often develop new hypotheses before using them to decide what phenomena to observe. See the article on Philosophy of science for more on this.

As stated above, there is no one "scientific method" that all scientists follow as an algorithm, and there is no consensus on what occupations and activities count as science. A liberal, descriptive conception of the scientific method accepts that creativity, genius, inspiration and new ideas may enter at any stage in the scientific process. What differentiates science from non-sciences is that such creativity is tested against experimental reality. Science depends on empirical methods to build a consensus among peers about which ideas are accurate, and which are not.

Adherents of the scientific method do not claim that there are any preset guidelines for the production of new hypotheses. The history of science is strewn with stories of scientists describing a "flash of inspiration", or a hunch, which then motivated them to look for evidence to support their assertion.

Scientists tend to look for theories that are "elegant" or "beautiful"; in contrast to the usual English use of these terms, scientists have a very specific meaning when they use these words. "Elegance" (or "beauty") refers to the ability of a theory to neatly explain all known facts as simply as possible.

In recent years, the scientific method and its underlying empirical methods has been studied by Thomas Kuhn. He suggested that sociological mechanisms were important in how science works. In this view, a scientific revolution occurs when scientists encounter anomalies which cannot be explained by the universally accepted paradigm within which scientific progress had thereto been made. Once new discoveries are made that cannot be reconciled with a current paradigm, and these results are repeatedly independently confirmed by other scientists, then the scientific community is forced to create a new paradigm in line with the evidence.

While many people hold that Kuhn was criticising science, many scientists themselves see Kuhn's work as merely describing how the scientific method has always worked.

Post-20th-century study on the scientific method has focused on quasi-empirical methods, e.g. peer review, spread of notations, which are the key common concern of philosophy of science and philosophy of mathematics. In the presentation of the 'ideal' scientific method that follows, one must keep in mind that many parties are simultaneously executing empirical methods and reproducing work of others, and that social and linguistic processes play key roles in deciding the degree of examination that any given hypothesis will receive in practice.

History is replete with examples of accurate theories ignored by peers, and inaccurate ones propagated unduly, due to social factors that no 'scientific method' would choose to promote - but which are inevitable aspects of being fallible social humans. Concepts like 'validating knowledge already gathered' or 'improving knowledge' and 'eliminating error' or 'bias' implies some kind of value system or moral core distinctions between 'good' and 'bad' are in effect. These are usually socially determined or at least socially censored.

Scientists vary on how 'real' their models of reality are - the traditional concern of philosophy of science itself. Extreme skeptics argue that no empirical methods are so truly accurate as to be able to 'validate' any given theory, and therefore all of science must be seen as quasi-empirical. In effect, they argue that mathematics is just another science, and science is just another human construction, and that the scientific method itself is a way that human cultures come to agree on facts, notations, and even predictions.

The scientific method begins with observation. Scientific observation often includes careful measurements. At this stage the disclosure and documentation of experimental and observational methods is of the utmost importance. These are what makes it possible for others to replicate the observations independently. Failure to disclose methods and techniques has led to several famous scandals as with Paul Kammerer[?]'s discredited work with toads. Such discipline is even more important when the evidence being presented or the hypothesis being supported have not been previously reported. The person who presents undocumented original material risks having his work peremptorily dismissed without any consideration at all

Scientists also try to use operational definitions of their measurements. That is, measurements and other criteria for observation are defined in terms of physical actions that can be performed by anyone, rather than being defined in terms of abstract ideas or common understanding. For example, the term "day" is useful in ordinary life and we don't have to define it precisely to make use of it. But in studying the motion of the Earth, you have to be more careful else your measurements be so sloppy as to be useless, so science makes two operational definitions of a day: a solar day is the time between observing the sun at a particular position in the sky and observing it in the same position the next time; a sidereal day is the time between observing a specific star in the night sky at a specific position, and that same observation made the next time. These are useful since they are slightly different as a result of how the Earth moves, and properly using one or the other avoids problems. In particular, you will come to notice that the length of the solar day varies over the course of a year; you can then make a new operational definition of mean solar day as the average of these and study further. And so on.

In the hypothetical stage, scientists use their own creativity (currently not well understood), or any other methods available, to invent possible explanations for the phenomenon under study. For some philosophers of science the most important aspect of an explanation is that it must be falsifiable, whereby a contrary fact from an experiment must be possible (in other words, if no experiment can ever demonstrate the hypothesis to be false, the hypothesis is unscientific though perhaps true).

The scientist should also be--but need not be and often is not--impartial, considering all known evidence, and not merely the evidence which supports the hypothesis being developed. This makes it more likely that the hypotheses formed will be relevant and useful.

Explanations should also be guided by the principle of Occam's Razor; i.e., the hypothesis should not contain redundant and unwarranted assumptions, or --according to some--any apparent complexity. For example, after a storm a tree is noticed to have fallen. Based on this evidence of "a storm" and "a fallen tree" a reasonable hypothesis would be "a lightning bolt has hit the tree," a hypothesis which requires only one assumption--that it was, in fact, a lightning bolt (as opposed to a strong wind or an elephant) which knocked over the tree. The hypothesis that "the tree was knocked over by marauding 200 meter tall space aliens" requires several additional assumptions (eg, concerning the very existence of aliens, their ability to travel interstellar distances and an alien biology that allows them to be 200 meters tall in terrestrial gravity) and is therefore inferior. Certainly more than one hypothesis can be entertained to explain the same phenomena, and some of them might even be complex and require 'too many' assumptions for comfort, but Occam's Razor is only a rule of thumb for quickly evaluating which hypotheses are likely to be fruitful; it is not a strict rule, nor an invariable aspect of the scientific method.

It was once thought that science was based on inductive reasoning; that is, if one observes the same thing many times without observing an exception, one can conclude from that observation alone that the phenomenon is consistent. This was the view of Francis Bacon and some other of the empiricists, for example. David Hume's critique of induction itself settled its use in validation or proof. In the modern understanding of scientific method, induction serves only as a means of suggesting hypotheses; these still must be tested by experiment and evaluated in the same way as other hypotheses.

The scientific method provides no firm guidelines for choosing between two equally possible hypotheses, when these hypotheses otherwise are equally simple, and equally fit the available evidence. In such a case, one must investigate the hypothesis which seems most likely. If there is no physical experiment to distinguish one hypothesis from another, then it cannot matter which one chooses to support. Either or both hypotheses may be correct, or at least acceptable until further data is available, and that could be used to falsify one or both.

Hypotheses are also considered superior to other possible ones if they have more predictive power; that is, if there are many possible observations one might make that would falsify the hypothesis. The hypothesis that "all matter turns into chocolate when no one is looking, and then turns back if anyone looks" cannot be refuted, since the very definition of the problem contradicts testing (ie, makes no testable prediction), and is therefore not a proper scientific hypothesis. A hypothesis that predicts that "light bends in a strong gravitational field" (ie, one aspect of Einstein's theory of general relativity) is a strong hypothesis as it suggests concrete measurements which can be conducted to support or refute the claim. Using the prior "fallen tree" example, the hypothesis 'predicts' that the fallen tree will exhibit scorch marks or similar markings consistent with a lightning strike, and that meteorological records of the storm are likely to show that lightning occurred.

Note that deductive reasoning is generally used to predict the results of the hypothesis. That is, in order to predict what measurements one might find if you conduct an experiment, treat the hypothesis as a premise, and reason deductively from that to some not currently obvious conclusion, then test that conclusion. For example, Einstein's equations implied that time operated differently than had been thought, but that the difference was one which could be tested only under conditions that humans had never seen. Assuming his model and the equations applying to it were accurate, and reasoning deductively from them, it was possible to see that a clock sent on a fast spaceship would slow down compared to an identical clock left on Earth, if Einstein's special relativity model were correct, while if it were wrong, the clocks should stay synchronized, or at least not go out of synch in the way predicted. In 1905, when Einstein published his first special relativity paper, spaceships were purely fantasy. They became less so after World War II and this test became possible. A sufficiently quickly moving clock (ie, in Earth orbit) does indeed slow down with respect to its stationary twin (ie, still on the surface of the Earth). Every such experiment since they became possible has shown the same effect.

Probably the most important and universal aspect of scientific reasoning is verification: every hypothesis must be tested by performing appropriate physical experiments and measuring the results. since measurements are inherently imperfect (from human involvement if nothing else), and since measuring equipment has been getting better and better, new measurements are often more precise than their predecessors. This is both useful as a practical matter (eg, in chemical engineering or planetary exploration), but have sometimes demonstrated previously unknown variations from currently accepted theory (eg, the CPT experiments of Yang and Lee in the 1950s which forced fundamental changes in much of particle physics). Ideally, the experiments performed should be fully described so that anyone can reproduce them, and many scientists should independently verify every theory with multiple experiments. This is known as reproducibility.

Scientists should also attempt to design their experiments carefully. For example, if the measurements to be taken are difficult or more than ordinarily subject to observer bias, one must be careful to avoid distorting the results by the experimenter's wishes. When experimenting on complex systems, one must be careful to isolate the effect being tested from other possible causes of the intended effect(this is called a controlled experiment). In testing a drug, for example, it is important to carefully test that the supposed effect of the drug is produced only by the drug itself, and not by the placebo effect or by random chance. Doctors do this with what is called a double-blind study: two groups of patients are compared, one of which receives the drug and one of which receives a placebo. No patient in either group knows whether or not they are getting the real drug; even the doctors or other personnel who interact with the patients don't know which patient is getting the drug under test and which is getting a fake drug (often sugar pills), so their knowledge can't influence the patients either.

Note, however, that "verification" may be a misleading word, in that we
don't really "confirm" or "verify" a hypothesis so much as we fail to
refute it. We do not understand enough about the natural world to be certain that our current understanding of it (or some part of it) is correct. There have been many instances in the history of science in which one or another important scientist announced that there was no more to discover about some subject. These announcements have been, sooner or later, uniformly embarrassing. We may indeed understand the fundamental nature of some natural phenomena, but we know of no way to realize this--even if true. A better word, perhaps, would be "check". Too many "final understandings" have been torpedoed to claim anything stronger.

Any hypothesis, no matter how respected or time-honored, must be discarded once it is contradicted by new reliable evidence. Hence all scientific knowledge is always in a state of flux, for at any time new evidence could be presented that contradicts long-held hypothesises. A classic example is the wave theory of light[?] -- although it had been held to be incontrovertible for many decades, it was refuted by the discovery of the photoelectric effect. The currently held theory of light holds that photons (the 'particles' of light) also behave as waves under some circumstances. In the earlier tree example, the lack of scorch marks or of reports of lightning, combined with reports of hurricane force winds would cause the original hypothesis to be re-evaluated as less probable and a new one ("The tree was knocked over by strong winds") to be proposed. Choosing between the two would require additional tests. Note, however, that the tree example involves "historical tests" and illustrates one of the differences between an experimental science (e.g., physics) in which the phenomena being investigated can be reproduced as needed (or as can be affored for some branches of physics) and an observational one (e.g., paleontology or stellar evolution in which the only available 'experiments' are those conducted by 'nature' and which we might be able to observe).

Further, the experiments that reject a hypothesis should be performed by as many different scientists as possible to guard against bias, misunderstanding, and fraud. Scientific journals use a process of peer review, in which scientists submit their results to a panel of fellow scientists (who may or may not know the identity of the writer) for evaluation. Scientists are rightly suspicious of results that do not go through this process; for example, the cold fusion experiments of Fleischmann and Pons were never peer reviewed--they were announced directly to the press, before any other scientists had tried to reproduce the results or evaluate their efforts. They have not yet been reproduced elsewhere as yet; and the press announcement was regarded, by most nuclear physicists, as very likely wrong. Proper peer review would have, most likely, turned up problems and led to a closer examination of the experimental evidence Fleischmann, Pons, et al believed they had. Much embarrassment, and wasted effort worldwide, would have been avoided.

The terms "hypothesis", "model", "theory" and, "law" are often used incorrectly when applied to scientific ideas. (Let alone that often a hypothesis becomes a dogma or a taboo issue by the passing of the centuries and the immense inertia represented by the huge number of its desperate supporters.)

In general a hypothesis is a contention that has not (yet) been sustained or refuted, as one or more predictions made from it have not yet been tested. However, once the predictive phase has been carried out (at least to some degree) and there is some experimental evidence that supports the hypothesis then it will often begin to be referred to as a "model".

Models and theories that have withstood the test of time (and many experimental tests), and that have not been falsified by credible, repeatable experimental evidence or observation, may eventually acquire the 'status' of a "law".

It is a fundamental tenet of the scientific method that all "results" are provisional, and this must include the so-called "laws". Newton's "law of gravitation" is a famous example of a "law" that has been found to be only a partially correct (see general relativity description of gravity and the behavior of matter in motion.

Uninformed observers often have the impression that laws discovered by science are immutable. This is not so. A "law of science" is just the best possible description of all known data, and not a divine decree.

Science makes extensive use of Mathematics. Observing and collecting measurements often requires the use of mathematics; hypothesizing and predicting may require extensive use of mathematics. Mathematical branches often used in science include Calculus and Statistics. A form of scientific method has been applied to mathematics itself since the time of Euclid.

One school of thought asserts that the scientific method (and science in general) relies upon basic axioms or "self-evident truths" such as realism and consistency. While it is true that many scientists believe these things and do assume them in their everyday work, the method itself does not rely on them: all such assumptions are just part of the hypotheses being tested, and many of them are subject to test as well. For example, one of the "common sense" ideas that scientists believed for a long time is that any measurable property of an object is something that exists in the object before it is measured, and our measurements are merely observations of that pre-existing condition; Quantum mechanics rejects this, because experiments have contradicted it.

Some believe that scientific principles have been "solidly" established, beyond question. Some scientists themselves may indeed feel that way, having come to rely upon many of the results of science without having done all the experiments themselves; after all, one cannot expect every individual scientist to repeat hundreds of years' worth of experiments. Many scientists even encourage an attitude of skepticism toward claims that contradict the current state of common knowledge; but that only means such claims must meet a higher burden before being accepted, not that they can never be accepted. In the extreme, some, including some scientists, may believe in this or that scientific principle, or even "science" itself, as a matter of faith in a manner similar to those of religious believers. However, neither science nor scientific method itself rely on faith; all scientific facts (i.e., measurements) and explanations (i.e., hypotheses) are subject to test, and will eventually be rejected as the best available hypothesis upon new evidence falsifying them. (See more under falsificationism.

This is the reason that political, religious, or social enforcement of scientific convictions is inherently pernicious. Examples include the Roman Catholic Church's action against Galileo's non-Aristotelian discoveries about the behavior of the planets (they violated some prestigious, and ancient, philosophical speculation the Church had promoted to dogma), and Stalin's support for Lysenko's biological and genetic beliefs (what was wrong with standard genetics in Stalin's view is not clear; Lysenko was either a deliberate con man or incapable of following standard genetics).

In any description of the scentific method, key themes of empiricism, that is knowledge based on observation, and rationalism, that is knowledge based on deductive reasoning become apparent. (See Philosophy of science). It is often stated that the natural sciences in our society owe their success to the diligent application of the scientific method. Its proponents claim that it is rational and logical. However, as in all areas of human endeavor, there is some debate as to its nature and utility. Proponents of the scientific method caricature its detractors as ultra-relativists, whereas some detractors caricature proponents as positivists, and consider that the scientific method does not adequately explain the success of science in our society.

Imre Lakatos showed how people studying the natural world have, throughout the ages, constructed historical accounts to suit their pet philosophies and methods. This "rational reconstruction", as it is known, of the history of science is then used to justify certain ideological assumptions, producing what might tentatively be called a mythology of science.

The philosopher Paul Feyerabend argued that descriptions of the scientific method often do not match how scientific discoveries have actually occurred in history. Feyerabend objected to any single prescriptive scientific method on the grounds that science has no single aim. Without a fixed ideology, or the introduction of religious tendencies, the only approach which does not inhibit progress (using whichever definition of progress you see fit) is "anything goes": "'anything goes' is not a 'principle' I hold [...] but the terrified exclamation of a rationalist who takes a closer look at history." (Feyerabend, 1975).

Feyerabend's criticisms have been used by some to argue that science does not tend toward the truth, that it has no advantage over other ways of examining the world, and that its intellectual output largely is a socio-historical accident of the culture and values of scientists. Feyerabend himself strongly opposed this conclusion:

"How can an enterprise {science} depend on culture in so many ways, and yet produce such solid results? ....Movements that view quantum mechanics as a turning-point in thought - and that include fly-by-night mystics, prophets of a New Age, and relativists of all sorts - get aroused by the cultural component and forget predictions and technology." (Source: Paul Feyerabend. Atoms and Consciousness', in Common Knowledge Vol. 1, No. 1 1992: 28-32)"

It is not the goal of science to answer all questions, nor even to 'explain' any phenomena which are not experimentally accessible. Science does not produce truth, it merely improves the currently best hypothesis about some aspect of reality. It is not a source of value judgements. It can certainly speak to matters of ethics and public policy by pointing to the likely consequences of actions; however, it can't tell us which of those consequences to desire or which is 'best'. What one projects from the currently most reasonable scientific hypothesis into other realms of interest is not a strictly scientific question and the scientific method offers no assistance for those who wish to do so. They often claim scientific justification, nevertheless.

In matters of public policy, the quality of 'scientific support' claimed for a position is generally inversely related to that position's benefit to the claimer. In short, if 'junk science' will help a position that will benefit me, only considerable ethical uprightness will prevent me from using it. Such ethical standards are regrettably less common than we would all hope. Since the audience (i.e., everyone for some such debates) is rarely in a position to independently evaluate the scientific support claimed by anyone, much 'junk science' has achieved prominence. Without mastering the underlying science, about the only thing the non-scientist can do is attempt to filter out economic and social interests, taking seriously only those who don't seem to have a stake in having one or another position adopted as a proxy for evaluating the quality of the science.

For instance, a chemical company caught dumping something in a local stream claims it has scientific support for the harmlessness of the dumping and therefore nothing should be done, certainly not at its expense, about the dumping. The local law provides that those who dump dangerous stuff should clean it up. Local environmentalists claim to have scientific support for the danger and that therefore the company should be compelled to clean up the contamination. What should local government do? How should the citizenry judge the government's performance? A first evaluation is probably to look to 'the science'. But, whose analysis is correct? Perhaps neither, but as a first attempt to decide between the two positions, the company's financial interest indicates that its scientific support need not be believed out of hand. It has a higher burden of 'disbelief' because of that interest. In such cases, governments often call for an independent scientific evaluation and announce they will take action based on that report. At which point, the dispute will change into an attempt to find 'independent' scientists who are believed to be likely to support one side or the other.

These disputes are often wholly unscientific since they are essentially economic or social, not scientific.